Optimal control problems are often too complex to solve analytically. Computational methods usually replace the continuous infinite dimensional problem by a finite dimensional discrete approximation. The talk will survey classical discretization techniques based on a Runge-Kutta approximation to the differential equations (an h-method) and then introduce recent approximations based on collocation at the roots of orthogonal polynomials (a p-method). The best approximations are often achieved using an hp-framework that combines the best features of both approaches. Numerical results using the GPOPS-II (General Pseudospectral Optimal Control Software package) will be presented.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems